On arithmetical algorithms over finite fields
Journal of Combinatorial Theory Series A
Mastrovito Multiplier for All Trinomials
IEEE Transactions on Computers
Reed-Solomon Codes and Their Applications
Reed-Solomon Codes and Their Applications
Modern Computer Algebra
New Systolic Architectures for Inversion and Division in GF(2^m)
IEEE Transactions on Computers
Error Correction Coding: Mathematical Methods and Algorithms
Error Correction Coding: Mathematical Methods and Algorithms
Fast rational function reconstruction
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
On the equivalence of the Berlekamp-Massey and the Euclidean algorithms for decoding
IEEE Transactions on Information Theory
A simple algorithm for decoding Reed-Solomon codes and its relation to the Welch-Berlekamp algorithm
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Design of the (248,216) Reed-Solomon decoder with erasure correction for Blu-ray disc
IEEE Transactions on Consumer Electronics
Adaptive packet-level interleaved FEC for wireless priority-encoded video streaming
Advances in Multimedia
Time complexity estimation and optimisation of the genetic algorithm clustering method
WSEAS Transactions on Mathematics
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There has been renewed interest in decoding Reed-Solomon (RS) codes without using syndromes recently. In this paper, we investigate the complexity of syndromeless decoding, and compare it to that of syndrome-based decoding. Aiming to provide guidelines to practical applications, our complexity analysis focuses on RS codes over characteristic-2 fields, for which some multiplicative FFT techniques are not applicable. Due to moderate block lengths of RS codes in practice, our analysis is complete, without big O notation. In addition to fast implementation using additive FFT techniques, we also consider direct implementation, which is still relevant for RS codes with moderate lengths. For high-rate RS codes, when compared to syndrome-based decoding algorithms, not only syndromeless decoding algorithms require more field operations regardless of implementation, but also decoder architectures based on their direct implementations have higher hardware costs and lower throughput. We also derive tighter bounds on the complexities of fast polynomial multiplications based on Cantor's approach and the fast extended Euclidean algorithm.